Reliability evaluation method considering electrothermal aging coupling of battery energy storage system

Abstract

The invention discloses a reliability evaluation method considering electric heating aging coupling of a battery energy storage system, which comprises the following steps: firstly, analyzing a hierarchical structure of the battery energy storage system, analyzing main factors influencing the reliability of the battery energy storage system, then respectively establishing an electric heating model and an aging model of the battery energy storage system, and analyzing a coupling relationship between the electric heating model and the aging model; and analyzing and calculating the reliability of the battery energy storage system considering the electric heating aging coupling. According to the method, a finer electrothermal aging model of the battery energy storage system is used for modeling, the coupling influence relationship among electrical, thermal and aging parameters is analyzed, so that the influence parameters of the battery energy storage system can be analyzed more accurately, and general generation function analysis is performed based on the more accurate influence parameters; and the reliability parameter of the battery energy storage system is calculated, so that the reliability of the battery energy storage system can be evaluated more accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of battery energy storage system performance evaluation, and in particular relates to a reliability evaluation method considering the electrical and thermal aging coupling of a battery energy storage system. Background Art

[0002] In response to global climate change, traditional power systems are accelerating their transformation and upgrading to new power systems with new energy as the main body. In this context, a large number of distributed clean energy represented by wind energy and solar energy are connected to the power grid, which brings new challenges to the safe, stable and economical operation of the power system, and the problem of large-scale grid connection and consumption of new energy is difficult to be solved. Against this background, battery energy storage systems are more widely used. They mostly use lithium-ion batteries. In the working process, they involve many disciplines such as electricity and thermodynamics. Their electrical characteristics, thermal characteristics, and aging characteristics are nonlinearly coupled. In addition, the working environment of battery energy storage systems is complex and the load conditions are changeable. It becomes more difficult to consider the reliability evaluation research of battery dynamics.

[0003] The traditional method of evaluating the reliability of battery energy storage systems is to analyze the capacity attenuation of the battery cells inside the battery energy storage system at room temperature, thereby completing the reliability evaluation of the battery energy storage system. However, this method has the following defects:

[0004] (1) At present, the traditional reliability assessment method of battery energy storage system ignores the thermal process inside the battery energy storage system, simplifies the internal electrothermal aging coupling process, and has low accuracy.

[0005] (2) Currently, the internal thermal process of battery energy storage systems mostly uses large-scale simulation software, which has high computational complexity and is not suitable for reliability analysis and calculation of large-scale battery energy storage systems. Summary of the invention

[0006] In view of the above-mentioned deficiencies of the prior art, the present invention provides a reliability assessment method considering the electrical and thermal aging coupling of a battery energy storage system, which comprehensively considers the coupling effects of the electrical parameters, thermal parameters, and aging parameters of the battery energy storage system to improve the reliability assessment accuracy of the battery energy storage system.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A reliability assessment method considering the electric and thermal aging coupling of a battery energy storage system comprises the following steps:

[0009] S1. Based on the working state and charging and discharging conditions of the battery cells in the battery energy storage system, the working parameters of the battery cells are calculated according to the charging and discharging currents; the working parameters include the state of charge, voltage and power of the battery cells;

[0010] S2. Calculate the heat generation, heat dissipation and heat transfer of the battery cell over time by combining the working parameters of the battery cell and the parameters of the heat dissipation medium and the heat transfer medium, and then iteratively calculate the working temperature of the battery cell;

[0011] S3. Calculate the aging rate of the battery cell based on the operating parameters and operating temperature of the battery cell, and then use the double exponential function model to build a model to calculate the available power and remaining capacity of the battery cell;

[0012] S4. Using the general generating function method, the remaining capacity and available power of the battery cells are discretized into a performance interval set and a corresponding probability set, and then the remaining capacity performance probability distribution and the available power performance probability distribution of the battery energy storage system are calculated and determined according to the series-parallel relationship of the battery cells in the battery energy storage system;

[0013] S5. Determine the reliability result of the battery energy storage system being able to meet the specified performance requirements based on the remaining capacity performance probability distribution and the available power performance probability distribution of the battery energy storage system.

[0014] Specifically, in step S1, the operating parameters of the battery system are calculated in the following manner:

[0015]

[0016] In the formula, SOC k , SOC k-1 are the battery system charge states at time k and time k-1 respectively; Q cell,k is the battery capacity of the battery cell at time k; I b,k-1 is the current of the battery at time k-1, which indicates charging when positive and discharging when negative; η is the Coulomb efficiency of the battery, which takes a value of 1 during charging and 0.98 during discharging; Δt is the time interval between adjacent moments;

[0017]

[0018]

[0019]

[0020] Where U b,k is the battery terminal voltage at time k; I b,k is the current of the battery cell at time k, which indicates charging when positive and discharging when negative; is the open circuit voltage of the battery cell at time k; U1 is the voltage across the RC branch in the first-order Thevenin equivalent circuit model of the battery cell at time k; R1 and C1 are the polarization resistance and polarization capacitance of the RC branch in the first-order Thevenin equivalent circuit model of the battery, respectively; R0 is the equivalent resistance in the first-order Thevenin equivalent circuit model of the battery; e is a natural constant;

[0021] The power output of the battery is:

[0022]

[0023] Specifically, in step S2, the operating temperature of the battery cell is calculated in the following manner:

[0024] First calculate the heat generation power q of each battery cell separately 产热 , heat dissipation power q 散热 and heat transfer power q 热传递 :

[0025]

[0026] In the formula, q 产热 is the heat generation power of the battery cell; q ir is the irreversible thermal power generated by the internal resistance of the battery; q re is the reversible thermal power generated by the battery entropy change; T temp is the ambient temperature; T cell,k is the battery cell temperature at time k; Indicates the open circuit voltage of the battery cell at time k Battery cell temperature T cell,k The derivation of

[0027] q 散热 =q 空气 +q 冷却板 ,q 空气 =h 空气 A(T cell,k -T temp ), q 冷却板 =h 冷却液 A(T cell,k -T f );

[0028] In the formula, q 空气 is the air convection heat dissipation power of the battery cell, q 冷却板 h is the cooling power of the cooling plate of the battery cell; 空气 is the convective heat transfer coefficient between the battery cell and the air, A is the convective heat transfer area of ​​the battery cell; h 冷却液 is the convective heat transfer coefficient between the coolant and the solid contact surface of the cooling plate in the cooling system of the battery cell, T fis the coolant temperature of the coolant in the cooling system of the battery cell;

[0029]

[0030] In the formula, J T is the heat flux density, κ is the thermal conductivity of air, L is the air gap length between adjacent battery cells, T cell,k,相邻 is the temperature of another battery cell adjacent to the battery cell at time k;

[0031] The iterative calculation method of the operating temperature of the battery cell at two adjacent moments is:

[0032]

[0033] Where, T cell,k+1 is the operating temperature of the battery cell at time k+1; C is the specific heat capacity of the battery cell, and m is the mass of the battery cell.

[0034] Specifically, in step S3, the aging rate of a single cycle of the battery cell is calculated according to the following formula:

[0035]

[0036] In the formula, SOC ref , T ref The preset reference state of charge for each battery cell; DoD k k is the discharge depth of the battery cell at time k; DOD1 , k DOD2 , k DOD3 is the discharge depth stress coefficient; k t is the time stress coefficient, representing the aging decay rate of the battery cell in the time interval Δt of each adjacent moment; k is the k value at moment k; k SOC is the stress coefficient of the charged state; k T is the temperature stress coefficient;

[0037] Then, calculate the battery cell's state of health SOH as follows: k , Available power P cell,k and the remaining capacity Q cell,k :

[0038]

[0039]

[0040]

[0041] In the formula, SOH k , P cell,k , Q cell,kThey represent the health status, available power per unit value and remaining capacity per unit value of the battery cell at time k respectively; is the rated capacity of the battery cell; Q cell,end is the end-of-life threshold capacity of the battery cell; is the rated output power of the battery, k r is the health state fitting coefficient; α and β are the attenuation fitting coefficients; N is the number of cycles of the battery cell.

[0042] Specifically, the step S4 is as follows:

[0043] For any i-th battery cell, the remaining capacity Q of the i-th battery cell at time k is calculated using the general generating function method. cell,k,i Discretized into a set of remaining capacity performance intervals containing G performance intervals And the corresponding probability set

[0044]

[0045] in, Indicates the jth remaining capacity performance interval of the ith battery cell at time k Respectively represent the remaining capacity performance range The lower and upper limits of Indicates that the i-th battery cell at time k falls within the j-th remaining capacity performance interval The probability of remaining capacity performance interval The probability distribution of the remaining capacity Q cell,k,i is a normal distribution with a mean of:

[0046]

[0047]

[0048] in, is the rated capacity of the i-th battery cell;

[0049] According to the remaining capacity performance intervals of the i-th battery cell at time k Calculate the corresponding available power performance range

[0050] Among them, Q cell,end,i is the end-of-life threshold capacity of the i-th battery cell; is the rated output power of the battery of the ith battery cell; then, the available power performance interval set containing G performance intervals is obtained And the corresponding probability set

[0051]

[0052]

[0053] in, It represents the jth available power performance interval of the i-th battery cell at time k, and its probability distribution also satisfies the normal distribution;

[0054] The battery energy storage system includes M parallel battery clusters, each of which includes N battery cells connected in series, and the remaining capacity performance probability distribution of each battery cluster is calculated. and the available power performance probability distribution It can be expressed as follows using the general generating function method:

[0055]

[0056] in, They represent the remaining capacity performance probability distribution and available power performance probability distribution of the lth battery cluster respectively; They represent the jth remaining capacity performance interval and the corresponding probability of the lth battery cluster at time k, respectively. The value is The smallest remaining capacity performance interval in The value is The probability corresponding to the smallest remaining capacity performance interval in ; They represent the jth available power performance interval and the corresponding probability of the lth battery cluster at time k, respectively. The value is The smallest available power performance range, that is The value is The probability corresponding to the smallest available power performance interval;

[0057] Then, the remaining capacity performance probability distribution of the entire battery energy storage system is calculated and the available power performance probability distribution It can be expressed as follows using the general generating function method:

[0058]

[0059] in, They represent the jth remaining capacity performance interval and the corresponding probability of the battery energy storage system at time k, They represent the jth available power performance interval and the corresponding probability of the battery energy storage system at time k,

[0060] Specifically, the step S5 is as follows:

[0061] According to the remaining capacity performance probability distribution and available power performance probability distribution of the battery energy storage system, as well as the specified performance requirement γ, the remaining capacity performance interval is calculated to meet the requirements. And the available power performance range The total probability of k is used to obtain the reliability parameter of the battery energy storage system at time k. As the reliability result of the battery energy storage system at time k:

[0062]

[0063] Reliability parameters The larger the value of is, the higher the reliability of the battery energy storage system at time k is.

[0064] Compared with the prior art, the present invention has the following beneficial technical effects:

[0065] The present invention discloses a reliability assessment method considering the electrothermal aging coupling of a battery energy storage system. First, the hierarchical structure of the battery energy storage system is analyzed, and the main factors affecting the reliability of the battery energy storage system are analyzed. Then, the electrothermal model and the aging model of the battery energy storage system are established respectively, and the coupling relationship between the two is analyzed, and then the reliability of the battery energy storage system considering the electrothermal aging coupling is analyzed and calculated. This method uses a more sophisticated electrothermal aging model of the battery energy storage system for modeling, analyzes the coupling influence relationship between electrical, thermal, and aging parameters, so that the influencing parameters of the battery energy storage system can be analyzed more accurately, and a general generating function analysis is performed based on more accurate influencing parameters to calculate the reliability parameters of the battery energy storage system, so that the reliability of the battery energy storage system can be evaluated more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0067] Figure 1 Flow chart of the method of the present invention.

[0068] Figure 2 Schematic diagram of the battery energy storage system structure.

[0069] Figure 3 It is the circuit diagram of the first-order Thevenin equivalent circuit model of the battery cell.

[0070] Figure 4 Schematic diagram of the topological structure of a battery cell in an embodiment.

[0071] Figure 5 This is a temperature distribution diagram of the battery cell in the embodiment when charging for one hour in summer.

[0072] Figure 6 This is a diagram showing the average temperature variation of a battery cell within one day in spring in the embodiment.

[0073] Figure 7 Graph showing the change of available capacity of a battery cell over time in an embodiment.

[0074] Figure 8 Calculation results of reliability index of battery cells in the embodiment.

[0075] Fig. 9 Calculation result of reliability index of battery energy storage system in the embodiment. DETAILED DESCRIPTION

[0076] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but only represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0077] The present invention provides a reliability assessment method considering the coupling of electric and thermal aging of battery energy storage systems. Figure 1 As shown, the following steps are included:

[0078] S1. Based on the working state and charging and discharging conditions of the battery cells in the battery energy storage system, the working parameters of the battery cells are calculated according to the charging and discharging currents; the working parameters include the state of charge, voltage and power of the battery cells;

[0079] S2. Calculate the heat generation, heat dissipation and heat transfer of the battery cell over time by combining the working parameters of the battery cell and the parameters of the heat dissipation medium and the heat transfer medium, and then iteratively calculate the working temperature of the battery cell;

[0080] S3. Calculate the aging rate of the battery cell based on the operating parameters and operating temperature of the battery cell, and then use the double exponential function model to build a model to calculate the available power and remaining capacity of the battery cell;

[0081] S4. Using the general generating function method, the remaining capacity and available power of the battery cells are discretized into a performance interval set and a corresponding probability set, and then the remaining capacity performance probability distribution and the available power performance probability distribution of the battery energy storage system are calculated and determined according to the series-parallel relationship of the battery cells in the battery energy storage system;

[0082] S5. Determine the reliability result of the battery energy storage system being able to meet the specified performance requirements based on the remaining capacity performance probability distribution and the available power performance probability distribution of the battery energy storage system.

[0083] The method of the present invention models the electric and thermal parameters and aging parameters of the battery energy storage system, designs a unified reliability analysis and calculation framework, and can quickly and accurately realize the calculation of the reliability parameters of the battery energy storage system while considering the coupling of the electric parameters, thermal parameters, and aging parameters. First, the hierarchical structure of the battery energy storage system is analyzed, and the main factors affecting the reliability of the battery energy storage system are analyzed. Then, the electric and thermal model and aging model of the battery energy storage system are established respectively, and the coupling relationship between the two is analyzed, and then the reliability of the battery energy storage system considering the electric and thermal aging coupling is analyzed and calculated. The method of the present invention comprehensively considers the coupling effects of the electric parameters, thermal parameters, and aging parameters of the battery energy storage system, and can effectively improve the reliability assessment accuracy of the battery energy storage system.

[0084] The scheme of the present invention is described in detail below.

[0085] 1. Battery energy storage system hierarchy

[0086] Battery Energy Storage System (BESS) uses batteries as energy storage carriers to store and release recyclable electrical energy. Its specific composition mainly includes battery system, control system, energy conversion system and other auxiliary equipment, such as Figure 2 As shown. The battery part of the battery energy storage system can be divided into battery cells, battery clusters and battery systems. Battery cells are connected in series to form a battery cluster (for the convenience of thermal management, the battery cells in the battery cluster may be connected in series in multiple battery packs), and multiple battery clusters are connected in parallel to form a battery energy storage system. The control system includes a thermal management system (TMS), a battery management system (BMS), an energy management system (EMS), etc. The energy conversion system mainly includes an energy storage converter (PCS), etc. Other auxiliary equipment includes electrical components, mechanical brackets, etc.

[0087] The battery system plays a key role in the battery energy storage system (BESS). As the core component of the energy storage system, the performance and stability of the battery system directly affect the reliability and operating life of the energy storage system. In long-term operation, the battery system may be affected by various factors such as cycle aging, thermal management failure and internal short circuit, which may lead to increased failure rate and reduced reliability. Therefore, the reliability analysis and calculation of the battery system is the core link to ensure the safe and efficient operation of the energy storage system.

[0088] 2. Electrothermal model of battery cells

[0089] The battery energy storage system is composed of battery cells. It is necessary to calculate the operating parameters (including state of charge, voltage, power) and thermal parameters (heat generation, heat dissipation, heat transfer) of all battery cells in order to prepare for subsequent aging status analysis and reliability analysis.

[0090] 2.1 Electrical parameter model

[0091] The state of charge (SOC) is the ratio of the remaining capacity to the nominal capacity of the battery cell. The calculation formula is discretized as follows:

[0092]

[0093] In the formula, SOC k , SOC k-1 are the battery system charge states at time k and time k-1 respectively; Q cell,k is the battery capacity of the battery cell at time k, in ampere-hours; I b,k-1 is the current of the battery at time k-1, a positive value indicates charging, and a negative value indicates discharging; η is the Coulomb efficiency of the battery, which takes a value of 1 during charging and 0.98 during discharging; Δt is the time interval between adjacent moments.

[0094] The terminal voltage of the battery cell is calculated using the first-order Thevenin equivalent circuit model. The equivalent circuit model is shown in the figure below: Figure 3 As shown, the electrical operating parameters of the battery cell are calculated based on the equivalent circuit model:

[0095]

[0096]

[0097]

[0098] Where U b,k is the battery terminal voltage at time k; I b,k is the current of the battery cell at time k, which indicates charging when positive and discharging when negative; is the open circuit voltage of the battery cell at time k, which is related to SOC, and the relationship between them is modeled based on the sigmoid function. U1 is the voltage across the RC branch in the first-order Thevenin equivalent circuit model of the battery cell at time k; R1 and C1 are the polarization resistance and polarization capacitance of the RC branch in the first-order Thevenin equivalent circuit model of the battery, respectively; R0 is the equivalent resistance in the first-order Thevenin equivalent circuit model of the battery; these equivalent parameters are known quantities that can be measured and decomposed. For example, for commonly used battery cells in industry, R0 can be taken as 6.071×10 -3 Ω, R1=6.071×10 -3 Ω, C1 = 7145F. e is a natural constant. K0 ~ K5, α1 ~ α4 are all model parameters of the first-order Thevenin equivalent circuit model, and these model parameters are all constants, among which K0 = 3.4002, K1 = 0.0080, K2 = 0.0785, K3 = -0.2150, K4 = -1.3032, K5 = 0.0891; α1 = -14, α2 = -18, α3 = 28, α4 = 40.

[0099] The output power of a battery cell is equal to the terminal voltage multiplied by the current. The current between the series-connected cells is the same, and the magnitude of the current depends on the charge and discharge scheduling instructions, but the terminal voltage of each cell is different, so the output power is different. The power output of a battery cell is:

[0100]

[0101] 2.2 Thermal model

[0102] 2.2.1 Battery Cell Heat Generation Model

[0103] The Bernardi battery heat generation model is used to calculate the battery temperature and establish a mathematical model of battery heat generation:

[0104]

[0105] In the formula, q 产热 is the heat generation power of the battery cell; q ir It is the irreversible heat power generated by the internal resistance of the battery and is the main factor in the heat generation of the battery; re is the reversible thermal power generated by the battery entropy change; T temp is the ambient temperature, which is 25°C; T cell,k is the battery cell temperature at time k; Indicates the open circuit voltage of the battery cell at time k Battery cell temperature T cell,k The derivation of .

[0106] 2.2.2 Battery Cooling Model

[0107] (1) Natural heat convection

[0108] q 空气 =h 空气 A(T cell,k -T temp )(7)

[0109] In the formula, q 空气 is the air convection heat dissipation power of the battery cell, h 空气 is the convective heat transfer coefficient between the battery cell and the air, and A is the convective heat transfer area of ​​the battery cell.

[0110] (2) Liquid cooling equivalent model

[0111] Considering the cooling plate heat dissipation method, according to Newton's cooling law, the convection loss of the battery through liquid cooling is calculated:

[0112] q 冷却板 =h 冷却液 A(T cell,k -T f )(8)

[0113] In the formula, q 冷却板 h is the cooling power of the cooling plate of the battery cell; 冷却液 T is the convective heat transfer coefficient between the coolant and the solid contact surface of the cooling plate in the cooling system of the battery cell. If the heat transfer capacity of the liquid is strong, the heat transfer coefficient is relatively high; f It is the coolant temperature of the coolant in the cooling system of the battery cell.

[0114] Thus, the heat dissipation power q of the battery cell is obtained 散热 =q 空气 +q 冷却板 .

[0115] 2.2.3 Battery heat transfer model

[0116] The battery cells in the battery energy storage system are closely arranged, with small air gaps between cells, and heat transfer is mainly carried out through conduction. Use Fourier's law to calculate the heat flux density and heat transfer:

[0117]

[0118] In the formula, J T is the heat flux density, κ is the thermal conductivity of air, L is the air gap length between adjacent battery cells, T cell,k,相邻 is the temperature of another battery cell adjacent to the battery cell at time k.

[0119] 2.2.3 Battery temperature calculation model

[0120] After obtaining the heat generation power q of the battery cell 产热 , heat dissipation power q 散热 and heat transfer power q 热传递 After that, the operating temperature of the battery cell at two adjacent moments can be iteratively calculated according to the following formula, so as to obtain the operating temperature of each battery cell at each moment:

[0121]

[0122] T cell,k+1 =T cell,k +ΔT cell (11)

[0123] Where, T cell,k+1 is the operating temperature of the battery cell at time k+1; C is the specific heat capacity of the battery cell, and m is the mass of the battery cell.

[0124] 3. Battery energy storage system aging

[0125] Based on the aforementioned electric and thermal model of the battery energy storage system, the electrical parameters and thermal parameters at each moment are calculated, and then the capacity attenuation status inside the battery energy storage system at each moment is calculated based on these parameters.

[0126] 3.1 Capacity decay model

[0127] The capacity decay of the battery energy storage system mainly includes calendar aging decay and cycle aging decay, and both aging modes are expressed as stress-related parameters. Four different dimensions of stress factors are considered: depth of discharge (DoD), time (t), state of charge (SoC), and temperature (T). Calendar decay is affected by the time, temperature, and SoC level stress dimensions, while cycle decay is affected by the depth of discharge, temperature, and average SoC stress dimensions. Considering two battery aging conditions, based on the coefficients and empirical models of each stress, the aging rate of the battery in a single cycle is obtained:

[0128]

[0129] In the formula, S DoD , S t , S SoC , S T They are the discharge depth stress factor, time stress factor, state of charge stress factor and temperature stress factor that affect battery attenuation. ref The preset reference state of charge of the battery cell can be 0.5, T ref The preset reference temperature for the battery cell can be 25°C. k k is the discharge depth of the battery cell at time k, which is the change in the battery's state of charge over a period of time. DOD1 , k DOD2 , kDOD3 is the discharge depth stress coefficient, which can be taken as k DOD1 =1.4×10 5 , k DOD2 =-5.01×10 -1 , k DOD3 =-1.23×10 5 ;k t is the time stress coefficient, representing the aging decay rate of the battery cell in each adjacent time interval Δt, k t =4.1410 -10 ; k is the k value at time k; k SOC is the stress coefficient of the charged state, which can be taken as k SOC =1.04; k T is the temperature stress coefficient, which can be taken as k T =6.93×10 -2 .

[0130] The available capacity of lithium-ion batteries will decrease as they run, according to the aging rate of the battery in each cycle. d,k , the remaining capacity of the battery cell is modeled as a double exponential function:

[0131]

[0132] In the formula, Q cell,k is the per-unit value of the remaining capacity of the battery cell at time k; N is the number of cycles of the battery cell; α and β are the attenuation fitting coefficients, and α can be taken as 5.75×10 -2 , β=121.

[0133] 3.2 Battery power attenuation model

[0134] The state of health (SOH) of a battery cell can be used to quantify the severity of the degradation of a battery cell. The health state of a cell can be calculated based on its remaining capacity:

[0135]

[0136] In the formula, SOH k Indicates the health status of the battery cell at time k; is the rated capacity of the battery cell; Q cell,end It is the end-of-life threshold capacity of the battery cell, which is generally 80% of the rated capacity of the battery.

[0137] The available battery power can be calculated using the following formula:

[0138]

[0139] Where P cell,kIndicates the per-unit value of the available power of the battery cell at time k; is the rated output power of the battery; k r is the health state fitting coefficient, which can be obtained by regression fitting of the linear relationship between ohmic internal resistance and SOH, and can be taken as k r =1.64356.

[0140] 4. Battery Energy Storage System Reliability Assessment Model

[0141] Based on the capacity attenuation and power attenuation calculated by the above model, combined with the universal generating function (UGF) method in reliability assessment, the continuous battery state parameters are discretized into interval values, thereby simplifying the calculation complexity and completing the reliability assessment of the battery energy storage system.

[0142] 4.1 Battery System Multi-State Model

[0143] Usually, the number of battery cells in a battery energy storage system can reach thousands. It is obviously impractical to measure the parameters of each battery, so it is necessary to introduce a multi-state model of the battery system.

[0144] Assume that the SOH of a battery cell can be divided into G discrete values. Each discrete value represents the SOH condition within a range (99.5% to 100% range, 99% to 99.5% range, ..., 0% to 0.5% range). The parameter matrix and corresponding probability matrix composed of the discrete state parameters of the battery cell are:

[0145] g i = {g i1 ,g i2 ,...,g ij ,...,g iG} (16)

[0146] p i ={p i1 ,p i2 ,...,p ij ,...,p iG} (17)

[0147] Collection i 、p i They represent the performance interval set and the corresponding probability set of the ith battery cell respectively; g ij represents the jth performance interval of the ith battery cell [g ij_low ,g ij_up ), g ij_low ,g ij_up Performance range The lower and upper limits of pij Indicates that the i-th battery cell falls in the j-th performance interval [g ij_low ,g ij_up ), and all probabilities are combined to form a probability set p j , and the sum of all elements in this set should be 1.

[0148] Therefore, the performance probability distribution of the battery cell based on SOH can be expressed as follows using the universal generating function method UGF:

[0149]

[0150] Where G is the number of performance intervals contained in the performance interval set.

[0151] Based on the above analysis, for any i-th battery cell, the remaining capacity Q of the i-th battery cell at time k is calculated using the general generating function method. cell,k,i Discretized into a set of remaining capacity performance intervals containing G performance intervals And the corresponding probability set

[0152]

[0153]

[0154] in, Indicates the jth remaining capacity performance interval of the ith battery cell at time k Respectively represent the remaining capacity performance range The lower and upper limits of Indicates that the i-th battery cell at time k falls within the j-th remaining capacity performance interval Here, the remaining capacity performance interval is set The probability distribution of the remaining capacity Q cell,k,i is a normal distribution with a mean of:

[0155]

[0156]

[0157] Therefore, the remaining capacity performance range The probability distribution of satisfies:

[0158] According to the remaining capacity performance intervals of the i-th battery cell at time k Calculate the corresponding available power performance range for:

[0159]

[0160] Among them, Q cell,end,i is the end-of-life threshold capacity of the i-th battery cell; is the rated output power of the battery of the ith battery cell; then, the available power performance interval set containing G performance intervals is obtained And the corresponding probability set

[0161]

[0162]

[0163] in, It represents the jth available power performance interval of the i-th battery cell at time k, and its probability distribution also satisfies the normal distribution.

[0164] 4.2 General generating function representation of battery system series-parallel structure

[0165] Assume that the battery energy storage system includes M parallel battery clusters, each battery cluster contains N battery cells in series. In order to better reflect the topological structure of the battery system, the battery system topological structure operator is defined as:

[0166]

[0167] At present, the topology of battery cells in battery energy storage systems is first connected in series and then in parallel. Therefore, it is necessary to start the analysis from the series calculation, and then analyze the parallel UGF parameters after obtaining the series UGF. In the calculation process of UGF, similar items with the same order can be combined together, and the commutative law and the associative law are also applicable to the calculation of UGF.

[0168] The system UGF of the series battery structure and the parallel battery structure can be calculated by using the corresponding series operator in formula (22), so the remaining capacity performance probability distribution of each battery cluster is and the available power performance probability distribution It can be expressed as follows using the general generating function method:

[0169]

[0170] in, They represent the remaining capacity performance probability distribution and available power performance probability distribution of the lth battery cluster respectively; They represent the jth remaining capacity performance interval and the corresponding probability of the lth battery cluster at time k, respectively. The value is The smallest remaining capacity performance interval in The value is The probability corresponding to the smallest remaining capacity performance interval in ; They represent the jth available power performance interval and the corresponding probability of the lth battery cluster at time k, respectively. The value is The smallest available power performance range, that is The value is The probability corresponding to the smallest available power performance interval;

[0171] Then, the remaining capacity performance probability distribution of the entire battery energy storage system is calculated and the available power performance probability distribution It can be expressed as follows using the general generating function method:

[0172]

[0173] in, They represent the jth remaining capacity performance interval and the corresponding probability of the battery energy storage system at time k, They represent the jth available power performance interval and the corresponding probability of the battery energy storage system at time k,

[0174] According to the general generating function method of battery series-parallel structure, the remaining capacity performance state distribution of the battery energy storage system is represented by and available power performance state distribution as follows:

[0175]

[0176]

[0177] 4.3 Calculation of reliability index of battery energy storage system

[0178] The reliability of a multi-state system is defined as the probability that the system's performance level is higher than the requirement. Assuming that the minimum performance requirement specified by the BESS is γ, the performance requirement γ is usually 75% to 80%. The system meets the performance requirement only when both the capacity state and the power state of the battery energy storage system meet the requirements, that is, and Therefore, after calculating the performance state and corresponding probability of the battery energy storage system, the remaining capacity performance interval that satisfies the remaining capacity performance probability distribution and available power performance probability distribution of the battery energy storage system and the specified performance requirement γ can be calculated. And the available power performance range The total probability of k is used to obtain the reliability parameter of the battery energy storage system at time k. As the reliability result of the battery energy storage system at time k:

[0179]

[0180] Reliability parameters The larger the value of is, the higher the reliability of the battery energy storage system at time k is.

[0181] The following is a further detailed description in conjunction with specific implementation methods:

[0182] Example:

[0183] In order to illustrate the effectiveness of this method more clearly and intuitively, the following verification description is given for this method.

[0184] by Figure 2 Taking the battery energy storage system shown in the figure as an example, the battery energy storage system consists of multiple battery packs. The thermal state of each battery pack is independent. Therefore, the battery pack (composed of m rows and n columns of cells) is used as the smallest thermal model unit to analyze the thermal model of the battery cells inside the battery pack, so as to calculate the temperature of each battery pack at each moment. The battery pack topology used in this case is as follows Figure 4 shown.

[0185] In the example, the daily charging start time is set at 2:00 and 14:00, the discharging start time is set at 8:00 and 20:00, and the expected charging and discharging time each time is 2 hours.

[0186] First, the internal temperature distribution diagram of the battery cell charged for 1 hour in summer is obtained as follows Figure 5 As shown. It can be seen that after one hour of charging, the temperature of the battery cells in the battery module is different. The temperature of the individual in the middle position is higher, while the temperature of the individual at the boundary position is lower. This is because the heat dissipation area of ​​the individual in the middle position is smaller, and there is more heat transfer, while the heat dissipation area of ​​the individual at the boundary position is larger, the number of adjacent individuals is smaller, and the heat transfer is less.

[0187] The average temperature change of the battery cell in spring within one day is shown in the figure below: Figure 6 As shown, it can be seen that the temperature of the battery is related to the charge and discharge state. During the charge and discharge state, the temperature of the battery rises rapidly, and when the battery is stationary, it will gradually dissipate heat until the ambient temperature.

[0188] The attenuation of battery capacity is mainly related to factors such as temperature, time, and state of charge. The change of battery available capacity over time is shown in the figure below: Figure 7 As shown in the figure, as the battery energy storage system charges and discharges, the battery capacity will continue to decay, and the environmental factors in the operating conditions will change, causing fluctuations in the capacity decay.

[0189] Assuming that a battery cluster consists of 9 battery cells connected in series and a battery energy storage system consists of 12 battery clusters connected in parallel, the reliability index is obtained according to UGF. The reliability index of the battery cell and the reliability index of the battery energy storage system as a whole are as follows: Figure 8 , Fig. 9 As shown, combined with the aforementioned battery available capacity attenuation diagram, it can be seen that when the battery in the battery system approaches the capacity threshold (generally 80% of the rated capacity), the reliability of the battery module and the battery system continues to decline. However, since the battery energy storage system is composed of multiple battery modules in parallel, its reliability is greater.

[0190] In summary, the present invention provides a reliability assessment method that takes into account the coupling of electric and thermal aging of a battery energy storage system. The method uses a more sophisticated electric and thermal aging model of the battery energy storage system for modeling, and analyzes the coupling influence relationship between electrical, thermal, and aging parameters, so that the influencing parameters of the battery energy storage system can be analyzed more accurately. Based on the more accurate influencing parameters, a general generating function analysis is performed to calculate the reliability parameters of the battery energy storage system, which can more accurately evaluate the reliability of the battery energy storage system.

[0191] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A reliability assessment method considering the electrothermal aging coupling of a battery energy storage system, characterized in that: The steps include: S1. Based on the working state and charging and discharging conditions of the battery cells in the battery energy storage system, the working parameters of the battery cells are calculated according to the charging and discharging currents; the working parameters include the state of charge, voltage and power of the battery cells; S2. Calculate the heat generation, heat dissipation and heat transfer of the battery cell over time by combining the working parameters of the battery cell and the parameters of the heat dissipation medium and the heat transfer medium, and then iteratively calculate the working temperature of the battery cell; S3. Calculate the aging rate of the battery cell based on the operating parameters and operating temperature of the battery cell, and then use the double exponential function model to build a model to calculate the available power and remaining capacity of the battery cell; S4. Using the general generating function method, the remaining capacity and available power of the battery cells are discretized into a performance interval set and a corresponding probability set, and then the remaining capacity performance probability distribution and the available power performance probability distribution of the battery energy storage system are calculated and determined according to the series-parallel relationship of the battery cells in the battery energy storage system; S5. Determine the reliability result of the battery energy storage system being able to meet the specified performance requirements based on the remaining capacity performance probability distribution and the available power performance probability distribution of the battery energy storage system.

2. The reliability assessment method considering the electrothermal aging coupling of the battery energy storage system according to claim 1 is characterized in that: In step S1, the operating parameters of the battery system are calculated in the following manner: In the formula, SOC k , SOC k-1 are the battery system charge states at time k and time k-1 respectively; Q cell,k is the battery capacity of the battery cell at time k; I b,k-1 is the current of the battery at time k-1, which indicates charging when positive and discharging when negative; η is the Coulomb efficiency of the battery, which takes a value of 1 during charging and 0.98 during discharging; Δt is the time interval between adjacent moments; Where U b,k is the battery terminal voltage at time k; I b,k is the current of the battery cell at time k, which indicates charging when positive and discharging when negative; is the open circuit voltage of the battery cell at time k; U1 is the voltage across the RC branch in the first-order Thevenin equivalent circuit model of the battery cell at time k; R1 and C1 are the polarization resistance and polarization capacitance of the RC branch in the first-order Thevenin equivalent circuit model of the battery, respectively; R0 is the equivalent resistance in the first-order Thevenin equivalent circuit model of the battery; e is a natural constant; The power output of the battery is:

3. The reliability assessment method considering the electrothermal aging coupling of the battery energy storage system according to claim 2 is characterized in that: In step S2, the operating temperature of the battery cell is calculated in the following manner: First calculate the heat generation power q of each battery cell separately 产热 , heat dissipation power q 散热 and heat transfer power q 热传递 : In the formula, q 产热 is the heat generation power of the battery cell; q ir It is the irreversible thermal power generated by the internal resistance of the battery; q re The reversible thermal power generated by the entropy change of the battery; T temp is the ambient temperature; T cell,k is the battery cell temperature at time k; Indicates the open circuit voltage of the battery cell at time k Battery cell temperature T cell,k The derivation of q 散热 =q 空气 +q 冷却板 ,q 空气 =h 空气 A(T cell,k -T temp ),q 冷却板 =h 冷却液 A(T cell,k -T f ); In the formula, q 空气 is the air convection heat dissipation power of the battery cell, q 冷却板 h is the cooling power of the cooling plate of the battery cell; 空气 is the convective heat transfer coefficient between the battery cell and the air, A is the convective heat transfer area of ​​the battery cell; h 冷却液 is the convective heat transfer coefficient between the coolant and the solid contact surface of the cooling plate in the cooling system of the battery cell, T f is the coolant temperature of the coolant in the cooling system of the battery cell; In the formula, J T is the heat flux density, κ is the thermal conductivity of air, L is the air gap length between adjacent battery cells, T cell,k,相邻 is the temperature of another battery cell adjacent to the battery cell at time k; The iterative calculation method of the operating temperature of the battery cell at two adjacent moments is: Where, T cell,k+1 is the operating temperature of the battery cell at time k+1; C is the specific heat capacity of the battery cell, and m is the mass of the battery cell.

4. The reliability assessment method considering the electrothermal aging coupling of the battery energy storage system according to claim 1 is characterized in that: In step S3, the aging rate of a single cycle of the battery cell is calculated according to the following formula: In the formula, SOC ref , T ref The preset reference state of charge for each battery cell; DoD k k is the discharge depth of the battery cell at time k; DOD1 , k DOD2 , k DOD3 is the discharge depth stress coefficient; k t is the time stress coefficient, representing the aging decay rate of the battery cell in the time interval Δt of each adjacent moment; k is the k value at moment k; k SOC is the stress coefficient of the charged state; k T is the temperature stress coefficient; Then, calculate the battery cell's state of health SOH as follows: k , Available power P cell,k and the remaining capacity Q cell,k : In the formula, SOH k , P cell,k , Q cell,k They represent the health status, available power per unit value and remaining capacity per unit value of the battery cell at time k respectively; is the rated capacity of the battery cell; Q cell,end is the end-of-life threshold capacity of the battery cell; is the rated output power of the battery, k r is the health state fitting coefficient; α and β are the attenuation fitting coefficients; N is the number of cycles of the battery cell.

5. The reliability assessment method considering the electrothermal aging coupling of the battery energy storage system according to claim 4 is characterized in that: The step S4 is specifically as follows: For any i-th battery cell, the remaining capacity Q of the i-th battery cell at time k is calculated using the general generating function method. cell,k,i Discretized into a set of remaining capacity performance intervals containing G performance intervals And the corresponding probability set in, Indicates the jth remaining capacity performance interval of the ith battery cell at time k Respectively represent the remaining capacity performance range The lower and upper limits of Indicates that the i-th battery cell at time k falls within the j-th remaining capacity performance interval The probability of remaining capacity performance interval The probability distribution of the remaining capacity Q cell,k,i is a normal distribution with a mean of: in, is the rated capacity of the ith battery cell; According to the remaining capacity performance intervals of the i-th battery cell at time k Calculate the corresponding available power performance range Among them, Q cell,end,i is the end-of-life threshold capacity of the i-th battery cell; is the rated output power of the battery of the ith battery cell; then, the available power performance interval set containing G performance intervals is obtained And the corresponding probability set in, It represents the jth available power performance interval of the i-th battery cell at time k, and its probability distribution also satisfies the normal distribution; The battery energy storage system includes M parallel battery clusters, each of which includes N battery cells connected in series, and the remaining capacity performance probability distribution of each battery cluster is calculated. and the available power performance probability distribution It can be expressed as follows using the general generating function method: in, They represent the remaining capacity performance probability distribution and available power performance probability distribution of the lth battery cluster respectively; They represent the jth remaining capacity performance interval and the corresponding probability of the lth battery cluster at time k, respectively. The value is The smallest remaining capacity performance interval in The value is The probability corresponding to the smallest remaining capacity performance interval in ; They represent the jth available power performance interval and the corresponding probability of the lth battery cluster at time k, respectively. The value is The smallest available power performance range, that is The value is The probability corresponding to the smallest available power performance interval; Then, the remaining capacity performance probability distribution of the entire battery energy storage system is calculated and the available power performance probability distribution It can be expressed as follows using the general generating function method: in, They represent the jth remaining capacity performance interval and the corresponding probability of the battery energy storage system at time k, They represent the jth available power performance interval and the corresponding probability of the battery energy storage system at time k, 6. The reliability assessment method considering the electric and thermal aging coupling of the battery energy storage system according to claim 1 is characterized in that: The step S5 is specifically as follows: According to the remaining capacity performance probability distribution and available power performance probability distribution of the battery energy storage system, as well as the specified performance requirement γ, the remaining capacity performance interval is calculated to meet the requirements. And the available power performance range The total probability of k is used to obtain the reliability parameter of the battery energy storage system at time k. As the reliability result of the battery energy storage system at time k: Reliability parameters The larger the value of is, the higher the reliability of the battery energy storage system at time k is.

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